"They opened fire toward IDF (army) troops that were guarding the workers (building the fence) in that area. Another force that was nearby... rushed to the area and targeted those three terrorists," she said.

"All three terrorists were killed."

She said the men were "very well armed and prepared" in terms of equipment, and were also wearing explosives belts.

"A very big terror attack was thwarted by the quick response of these soldiers," Leibovich said, ruling out the possibility that any further armed men had infiltrated Israeli territory.

Border security incidents have increased over the past 18 months as a wave of lawlessness has gripped the Sinai since the overthrow of veteran Egyptian president Hosni Mubarak.

On June 18, at least three armed men cross the border from Sinai and ambushed two cars carrying Israeli construction workers, killing one and sparking a firefight with the army in which two of the attackers died. The third fled back to Egypt.

The most serious incident so far took place in August 2011, when another group of armed men from Sinai infiltrated southern Israel and staged a series of ambushes that killed eight Israelis.

Israel has accused Gaza-based groups of using the Sinai as a launchpad for cross-border attacks and has demanded that Egypt crack down on Islamist elements in the lawless peninsula.

In a bid to prevent such attacks, as well as the entry of illegal immigrants from Africa, Israel has been working on construction of a massive steel barrier along its border with the Sinai.